Today we will…
Assess if the model would produce data similar to what was observed.
Danger
Predictive checks do not make predictions for new observations.
Bayes!
Why do we care? An assessment of “subjective” choices!
Requirements of a “good” regression model (LINE)
Fit a regression model to observed data.
Obtain Predictions from the model and add random errors to the predictions.
Compare simulated data to observed data.
Iterate!
lmpredict + rnormlmMeasure “similarity” – \(R^2\) proportion of variability explained
Similarity Measures
Could also use correlation (\(r\)), size of the sum of squared errors (\(SSE\)), or the estimate of \(\hat \sigma\) (\(RMSE\))
mapgeom_histToday we will…